I am teaching mathematics for kids. Some of them are so lazy in thinking. They often answer my questions without thinking. And some of them also early decide that they will be artists, dancers, athletes, house-wives, etc so they don't need mathematics.

You could attract them with incentives and give special status to those who answered correctly. This incentive should not cost you anything like having a class leader for the day who answered maximum number of queries correctly the day before.
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Mukesh KamathSep 26 '13 at 17:56

@MukeshKamath That's a valid answer, but doesn't it motivate the motivated? If someone sees no value in maths or worse, is struggling, they're just going to accept that they will never be class leader and become even more demotivated. A more persistent "level-up" system, where as you progress you get to "apprentice" or "journeyman" seems like it would help more.
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dewordeSep 27 '13 at 9:09

5 Answers
5

I have had some success (in an unpaid, friend of the family or parent of the child's friend kind of way) with the following approach:

Stop referring to them, even inside your own head as lazy-to-think. While that is one possible explanation for them not answering, or blurting out any old number without working it out first, there are plenty of others: they are quite likely afraid and a little bit lost, unsure where to start. Your mental model of their motivation is really important. Make an effort to change it.

Look into yourself to find out why you like knowing (not learning, but where you are now knowing) the math you are trying to teach them. Is it fun? Can it prevent people from ripping them off with rent-to-buy or similar schemes? Will it help them get a job?

Share your enthusiasm with them. When it's time to teach them a technique, tell them why you are teaching it. (For example with much younger children, they learn to multiply because it's way quicker than adding over and over again.)

Understand that there are many ways of learning: that some kids hate word problems (and some adults too - a grandparent helping with homework complained to me that you had to understand farming to do the problems; you didn't, but getting past "if each cow needs 1/4 bale of hay and there are 12 cows how much hay do you need?" was impossible for the lifelong citydweller who couldn't find the math problem in there) while others hate equations but can do fractions blazingly fast if they are presented as involving money or sharing a pile of candies among friends. Mix it up and offer a variety. Consider using tactile learning aids like piles of lego for those who prefer to work things out their way.

Give them opportunities to succeed. Don't count their failures. It doesn't matter how many tries they needed to master something, it matters that they have mastered it. In martial arts classes the belt doesn't come with a little sticker on it that says "failed first two evaluations for this belt" and nor should whatever certificates or milestone acknowledgements you give the students.

Be open to the possibility that more than one answer is right. We asked a very young child who was doing sequences at school (eg 1, 4, 7, 10, ... what is next) to try 1, 4, 9, 16 and to our surprise the formula we were given was not "square of 1, 2, 3," but rather "add 3, then add 5, then add 7" and what's more this is in fact a completely correct answer (up to any value of i you want) which we ended up proving by drawing squares on a piece of paper. Don't force them to use your technique to solve problems.

Enjoy them. Enjoy watching their minds open to new things. Enjoy thinking of all the doors that will be open to them as adults when they are not afraid of math and they are good at it. And, I'm sure, enjoy all the new students you will have when word gets around that classes with PGFTricks are great fun.

+1 for stop thinking of them as lazy!
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balanced mamaOct 29 '13 at 16:27

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Excellent answer. I would add give them collaborative work - it is the future in business and two brains build knowledge faster than one on its own. Also give them projects that will require math at some point, and when they get to where they need it, help them learn it.
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MJ6Nov 3 '13 at 2:35

Chrys' Answer covers most of the ground I was going to, but one suggestion might be gamification.

From what you've said, some children see no value in going beyond basic maths, and while you might be able to convince them that those jobs they plan for require maths (good luck being a householder who can't balance a monthly budget), that's not always valid, and they can easily see counter-examples. It's even arguable that they're right and that the time spent learning maths is less valuable than focusing on what they're actually interested in (although I believe maths is interesting and fulfilling and that at least basic add/sub/mult/div is essential for day-to-day living, I can't dispute that most people can and do live happily in an algebra-free environment, let alone a calculus-free one).

So what you need to do is add "created" value to replace the "inherent" value that's lacking for them, and creating a game around it is one of the best ways to do that. (Hell, that's what a game does)

As an example, create a set of age-appropriate levels, with a set of SMART goals for those levels.

For example, everyone starts at a base level, and gains "experience" by answering questions in class, by getting above a certain grade in homework, and by being helpful in other ways such as staying behind to help clear (which gives kids who aren't as proficient a way to mitigate their struggling). The goals get more challenging as you progress (for example, XP would only be given for a 90%+ on a "Craftsman's" homework, whereas a "Novice" would get XP for any passing grade, they'd just get more for a 90%+.

As they rise in level, they get status and possibly first crack at whatever treats go on at the school (although this can backfire, see below), but you also have responsibilities to help out with other level students (Being seen as responsible and valued is a treat in itself for many children). This can be layered over a normal course pretty cleanly, as all you need to do is keep track of the XP.

Other benefits include being able to clearly see which children are struggling, being able to tailor for specific students in specific cases, and most importantly of all, a constant feeling of progress (normal grading being a bit prone to "you're only as good as your last grade").

Note that this is about competing against the tasks you need to accomplish, not against other students. Let them share their current XP/level if they want to, but don't have a "league".

How other students do should not affect your XP gain for several reasons, but the most important is that that kind of competition only "motivates the motivated". If you are regularly getting 10% lower grades than the more proficient students (who, for example, may have more supportive parents, private tuition, or simply a less stressful journey home, or who may actually be naturally more comfortable with maths), your reaction is more likely to be "fine he can have it", especially as they progress further. By making it about improving on your previous achievements, they've always got an achievable task, naturally tailored for them. As a bonus, this means that this technique can also be used even when there's only one student.

Obviously this alone takes a bit of work to manage, but if you're interested in deeper solutions, I can heartily recommend "Reality is Broken" by Jane McGonigal as a primer on this stuff (as well as a good read), and this video by the Extra Credits team. The video covers a lot of the stuff I did above, as well as mentioning a test case, and gives some great ideas for using the class dynamics to support and enthuse weaker students.

some of them also early decide that they will be artists, dancers, athletes, house-wives, etc so they don't need mathematics.

Involve their goal/hobbies/interests in your teaching. There is a high level of opportunity there. Applied mathematics are probably the key for most people having issues with formal mathematics.

You can start by finding problems related to each discipline :

use of the golden ratio in art ;

see James Snell's comment below for suggestions about dance ;

what is the best angle to throw a javelin (physics is involved here as well, but anyway) ;

finding proportions in cooking recipes ;

Fibonacci series in nature ;

etc.

The forementioned examples may only apply as recreational topics since they may differ from mathematical topics you have to teach, but recreational topics are useful to focus the attention and trigger an interest. You can also involved more generic (i.e. not interest-focused) mathematical games.

Then, for each student and for each mathematical topic you have to teach, ask yourself : "how can this topic be applied to this student's interests ?". Beware that just replacing apples and oranges by paintbrushes and javelins probably won't lead you very far. In most cases you'll have to find something more sophisticated.

Finally, when you are happy with a mathematical problem, even if it's aimed towards a particular interest, do not hesitate to present it to students with other interests. It's likely that they will be interested in applied mathematics even though it's not related to their favorite topic.

Mathematics are hidden everywhere in the real world. Therefore to make mathematics interesting is just a matter of finding the most adapted magnifying lens for each individual.

Dancing is quite easy for young ones since music and dance is entirely about maths. Counting out steps, how many to the front of the stage, how many times do you have to repeat a set of steps. Making patterns. How big an area do you need to perform a routine. How many tickets...
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James SnellNov 2 '13 at 19:14

Is it worth reversing the question back onto yourself... asking yourself "Why am I so lazy at teaching?" That's not to say you are lazy, but being good at a subject and being good at teaching it aren't even the same ballpark. So what are your roadblocks to getting through to them.

At ages 12-15 they're starting to enter the adult world and in a private tuition setting you should have good opportunity to reason with them to appreciate why each one isn't motivated and what their challenges are. Is there some tension there that they need to break. Is the technique you're using appropriate for them.

If they're just guessing then divert the session to explore the probability of how likely they are to be correct just by guessing. Explore with them how close their guesses are.

Can you take a break from maths as a rote subject to concentrate on getting around the roadblocks. For example would a project to explore how their role models use maths be valuable?